Time Machine Folder

Last month I bought a new 4 TB hard drive dedicated for Time Machine. To my surprise when I installed the drive, my Mac only saw 2.2 TB of it. Found out it was an external enclosure issue. So I ordered a new enclosure that can handle 4TB drives and now I'd like to take the hard drive out of the old enclose and switch it to the new one. Problem is the hard drive was formatted up to 2.2 TB so I'm going to need to reformat it for the full 4TB. I want to save the (current) Time Machine folder so that I don't lose all of the data it already has stored. Where is this data located, and is there any special procedure to "transplanting" that data onto the newly formatted 4TB drive? Thanks